Practice question · Sort into groups
Sort each set of vectors by whether it is linearly independent.
Groups: Independent · Dependent
- {(1, 0), (0, 1), (1, 1)}
- {(0, 0), (1, 3)}
- {(1, 2), (2, 4)}
- {(1, 0, 0), (0, 1, 0)}
- {(1, 1, 0), (0, 1, 1), (1, 2, 1)}
- {(1, 0), (0, 1)}
Hints
- Three quick disqualifiers: a zero vector, a visible multiple, or more vectors than dimensions.
- For the last set, add the first two vectors and compare with the third.
Show the answer
Independent: {(1, 0), (0, 1)}, {(1, 0, 0), (0, 1, 0)}
Dependent: {(1, 2), (2, 4)}, {(1, 0), (0, 1), (1, 1)}, {(0, 0), (1, 3)}, {(1, 1, 0), (0, 1, 1), (1, 2, 1)}
Why
The last set is the important one: no vector there is a multiple of another, yet (1,1,0) + (0,1,1) = (1,2,1), a nontrivial combination giving zero when moved to one side. Dependence means SOME combination vanishes, not that two vectors are parallel.
Practise Linear Independence
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
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